Question

The cost of fencing a circular field at the rate of Rs 24 per metre is Rs 5280. The field is to be ploughed at the rate of Rs 0.50 per m². Find the cost of ploughing the field (Take pi = 22/7 ).

Answer 1

Solution : Length of the fence (in metres) = Total cost / Rate = 5280/24 = 220
So, circumference of the field = 220 m
Therefore, if r metres is the radius of the field, then
2πr = 220

or, 2 × 22/7× r = 220
or, r = (220 × 7)/(2 × 22) = 35

i.e., radius of the field is 35 m.

Therefore, area of the field = πr² = 22/7 × 35 × 35 m² = 22 × 5 × 35 m²

Now, cost of ploughing 1 m² of the field = Rs 0.50
So, total cost of ploughing the field = Rs 22 × 5 × 35 × 0.50 = Rs 1925